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The sophisticated structure of Convolutional Neural Network (CNN) allows for outstanding performance, but at the cost of intensive computation. As significant redundancies inevitably present in such a structure, many works have been…
This is a tutorial on tabular parsing, on the basis of tabulation of nondeterministic push-down automata. Discussed are Earley's algorithm, the Cocke-Kasami-Younger algorithm, tabular LR parsing, the construction of parse trees, and further…
We present the Unified Form Language (UFL), which is a domain-specific language for representing weak formulations of partial differential equations with a view to numerical approximation. Features of UFL include support for variational…
Though modern neural networks have achieved impressive performance in both vision and language tasks, we know little about the functions that they implement. One possibility is that neural networks implicitly break down complex tasks into…
For a class L of languages let PDL[L] be an extension of Propositional Dynamic Logic which allows programs to be in a language of L rather than just to be regular. If L contains a non-regular language, PDL[L] can express non-regular…
We extend Antimirov's partial derivatives from regular expressions to $\mu$-regular expressions that describe context-free languages. We prove the correctness of partial derivatives as well as the finiteness of the set of iterated partial…
In the previous work, we have given a novel, game-semantic model of computation in an intrinsic, non-inductive and non-axiomatic manner, which is similar to Turing machines but beyond computation on natural numbers, e.g., higher-order…
This paper presents and analyzes an incremental algorithm for the construction of Acyclic Non-deterministic Finite-state Automata (NFA). Automata of this type are quite useful in computational linguistics, especially for storing lexicons.…
This paper exhibits a series of semantic characterisations of sublinear nondeterministic complexity classes. These results fall into the general domain of logic-based approaches to complexity theory and so-called implicit computational…
Machine learning classifiers' capability is largely dependent on the scale of available training data and limited by the model overfitting in data-scarce learning tasks. To address this problem, this work proposes a novel framework of Meta…
The use of non-deterministic functions is a distinctive feature of modern functional logic languages. The semantics commonly adopted is call-time choice, a notion that at the operational level is related to the sharing mechanism of lazy…
Marginalization -- summing a function over all assignments to a subset of its inputs -- is a fundamental computational problem with applications from probabilistic inference to formal verification. Despite its computational hardness in…
This paper presents a methodology for ensuring that the composition of multiple Control Barrier Functions (CBFs) always leads to feasible conditions on the control input, even in the presence of input constraints. In the case of a system…
In single-core processors, concurrency requires that multiple processes be interleaved into a single thread of execution by a scheduler. The language-theoretic operation that corresponds to this is the shuffle of two languages: the set of…
The reduction algorithms for functional determinants of differential operators on spacetime manifolds of different topological types are presented, which were recently used for the calculation of the no-boundary wavefunction and the…
We study Turing machines that are allowed absolutely no space overhead. The only work space the machines have, beyond the fixed amount of memory implicit in their finite-state control, is that which they can create by cannibalizing the…
Computer science students often struggle with abstract theoretical concepts, particularly in introductory courses on theoretical computer science. One such challenge is understanding context-free languages and their various representations.…
Control laws derived from Control-Lyapunov Functions (CLFs) offer an efficient way for generating near-optimal many-revolution low-thrust trajectories. A common approach to constructing CLFs is to consider the family of quadratic functions…
We analyze integral representation and $\Gamma$-convergence properties of functionals defined on \emph{piecewise rigid functions}, i.e., functions which are piecewise affine on a Caccioppoli partition where the derivative in each component…
How to usefully encode compositional task structure has long been a core challenge in AI. Recent work in chain of thought prompting has shown that for very large neural language models (LMs), explicitly demonstrating the inferential steps…